diff --git a/Modules/_io/fileio.c b/Modules/_io/fileio.c
--- a/Modules/_io/fileio.c
+++ b/Modules/_io/fileio.c
@@ -547,14 +547,14 @@ fileio_readinto(fileio *self, PyObject *
 }
 
 static size_t
-new_buffersize(fileio *self, size_t currentsize)
+new_buffersize(fileio *self, size_t currentsize
+#ifdef HAVE_FSTAT
+               , off_t pos, off_t end
+#endif
+               )
 {
 #ifdef HAVE_FSTAT
-    off_t pos, end;
-    struct stat st;
-    if (fstat(self->fd, &st) == 0) {
-        end = st.st_size;
-        pos = lseek(self->fd, 0L, SEEK_CUR);
+    if (end != -1) {
         /* Files claiming a size smaller than SMALLCHUNK may
            actually be streaming pseudo-files. In this case, we
            apply the more aggressive algorithm below.
@@ -579,9 +579,14 @@ new_buffersize(fileio *self, size_t curr
 static PyObject *
 fileio_readall(fileio *self)
 {
+#ifdef HAVE_FSTAT
+    struct stat st;
+    off_t pos, end;
+#endif
     PyObject *result;
     Py_ssize_t total = 0;
     int n;
+    size_t newsize;
 
     if (!_PyVerify_fd(self->fd))
         return PyErr_SetFromErrno(PyExc_IOError);
@@ -590,8 +595,23 @@ fileio_readall(fileio *self)
     if (result == NULL)
         return NULL;
 
+#ifdef HAVE_FSTAT
+#if defined(MS_WIN64) || defined(MS_WINDOWS)
+    pos = _lseeki64(self->fd, 0L, SEEK_CUR);
+#else
+    pos = lseek(self->fd, 0L, SEEK_CUR);
+#endif
+    if (fstat(self->fd, &st) == 0)
+        end = st.st_size;
+    else
+        end = -1;
+#endif
     while (1) {
-        size_t newsize = new_buffersize(self, total);
+#ifdef HAVE_FSTAT
+        newsize = new_buffersize(self, total, pos, end);
+#else
+        newsize = new_buffersize(self, total);
+#endif
         if (newsize > PY_SSIZE_T_MAX || newsize <= 0) {
             PyErr_SetString(PyExc_OverflowError,
                 "unbounded read returned more bytes "
@@ -630,6 +650,9 @@ fileio_readall(fileio *self)
             return NULL;
         }
         total += n;
+#ifdef HAVE_FSTAT
+        pos += n;
+#endif
     }
 
     if (PyBytes_GET_SIZE(result) > total) {